Problem: The grades on a geometry midterm at Oak are normally distributed with $\mu = 79$ and $\sigma = 3.5$. Luis earned a n $88$ on the exam. Find the z-score for Luis's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Luis's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{88 - {79}}{{3.5}}} $ ${ z \approx 2.57}$ The z-score is $2.57$. In other words, Luis's score was $2.57$ standard deviations above the mean.